Abstract
Let $\{T_{t}:t\in{\bf R}\}$ be a measure preserving flow in a probability measure space $(\Omega, {\cal A},\mu)$, and $\{F_{t}:t\in {\bf R}\}$ be a family of real-valued measurable functions on $(\Omega,{\cal A},\mu)$ such that $F_{t+s}=F_{t}+F_{s}\circ T_{t}$ (mod $\mu$) for all $t,\, s \in {\bf R}$. In this paper we deduce necessary and sufficient conditions for the existence of a real-valued measurable function $f$ on $\Omega$, with $f\in L_{p}(\Omega,\mu)$ where $0\leq p\leq \infty$, such that $F_{t}=f\circ T_{t}-f$ (mod $\mu$) for all $t\in {\bf R}$. Related results are also obtained. These may be considered to be continuous parameter refinements of the recent discrete parameter results of Alonso, Hong and Obaya concerning additive real coboundary cocycles.
Citation
Ryotaro Sato. "ERGODIC PROPERTIES OF CONTINUOUS PARAMETER ADDITIVE PROCESSES." Taiwanese J. Math. 7 (3) 347 - 390, 2003. https://doi.org/10.11650/twjm/1500558393
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